A detailed Monte Carlo investigation of the structural changes of the framework of sodium zirconium phosphate, [Zr2P3O12](-),-NASICON (acronym for Na-SuperIonic CONductor)-accommodating alkali ions of varying sizes (Li+, Na+, K+, Rb+ and Cs+) is carried out over a range of temperatures. Simulation results are critically compared with the structural models proposed earlier and available experimental results. Anisotropic changes of the rhombohedral cell parameters-a contracts while c expands with the size of the alkali ion substituted-is observed in good agreement with previous experimental results. The mechanism of anisotropic variation of lattice parameters involves dominantly, coupled rotations of the polyhedra as proposed by Alamo and co-workers. It is, however, observed that the distortions of the PO4 tetrahedra and ZrO6 octahedra are significant, and accounts for nearly one-third of the total change in a and c-parameters as the size of the alkali ion increases. This suggests that 'rigid' polyhedral models, permitting only angular distortions of the polyhedra, are of limited quantitative applicability in these solids. The same mechanism is found to be responsible for the low/anisotropic thermal expansion of these solids. Evidence that the polyhedral rotations are dynamic, opposed to a static-frozen-in disorder, is provided.